PSGarak
Posts: 834
4/15/2017
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Fallen London is a game about capitalist space-bats, the things they bought, and the people they bought them from. It is set in a cosmology where one of the protagonists is a literal marketplace. It is therefore no surprise that we, the players of Fallen London, spend much of our time thinking about the best ways for our characters to earn currency.
The most common method is EPA: Echoes per Action. I believe this method has limitations. Several others have voiced this opinion as well. I've been noodling on an idea for a replacement for a while, but after the recent discussions attempting to figure out which Expedition is the most profitable, I've finally decided to write out my thoughts. I hope that they join with other people's thoughts, and then everybody will have even better thoughts. Then a giant crab will give us money for them, or something.
First, I will illustrate a problem that I see with EPA.
A Highly Contrived Example
Imagine there is a one-time, non-repeatable choice that you are given (say, the conclusion of a one-time storyline). The two options are as follows, and are given whimsical names to make them easier to refer to later:
- Pebble: Spend one Action to gain ten Echoes
- Boulder: Spend ten Actions to gain fifty Echoes
Which option should you choose?
EPA would tell you that Pebble is the better option: It has an EPA of 10, compared to 5 for Boulder. But, this does not align with my intuition, and it may not align with yours. Fifty is, like, a lot of Echoes. Shouldn't that matter more? Sure, it takes more Actions to claim the reward, but isn't it still the better option?
One way of looking at this situation is that compared to Pebble, choosing Boulder will gain forty Echoes, and cost nine Actions. Should you spend nine Actions for Forty Echoes? One would think yes. So perhaps EPA has lead us astray.
Let's dig in just a little further: What is the value of nine actions? The answer depends on what you would do with those Actions if given the choice. And for most players, the answer is simple: Affair of the Box. So let's normalize the Action cost of each option by spending ten Actions on each, using Affair of the Box as the "replacement" Action when we need to, and see how much total money we make:
- Pebble: Ten echoes plus nine plays of AotB @ 1.64 EPA, for a total of 26.4 Echoes.
- Boulder: Fifty Echoes, straight-up.
Clearly, Boulder is the more profitable option. Given the same opportunities and the same resource expenditure, our hypothetical character comes out ahead by 23.6 Echoes.
Where EPA Goes Wrong
In short, EPA only makes sense as a metric for choices that are limited by Actions. In other words, it is useful for evaluating grinds. For something that is not limited by Actions, it doesn't make sense to use Actions as the denominator.
When presented with options that are limited by Cards, or Favors, or something similar, EPA will penalize options that require more Actions to cash in. But the true measure of profitability is actually the Opportunity Cost, i.e. "What could I have done instead?"
A New Metric: EOR
I propose a new metric named Echoes Over Replacement, abbreviated EOR, which is pronounced the same as Eeyore, the plush ungulate who is the second-best character voiced by Peter Cullen. EOR is applied to an Choice, which is enabled by an Opportunity such as a Card, or the gain of a Favor, and is used to evaluate how much money you will actually gain as a result of that Choice. EOR is calculated as:
EOR = E - (A * R)
E is the Echoes you stand to gain by taking your choice. A is the Action cost of your Choice. Either or both of these may be Expected Values, if there is probability involved.
R stands for Replacement, and is the EPA value of whatever grind you would be doing otherwise. For most end-game players, R is 1.64 from Affair of the Box. Players with access to Spirifage or the Goat-Demon grind may have higher values for R, but I will be assuming AotB for simplicity.
EOR is, very simply, the extra Echoes you make from your Choice instead of grinding Affair of the Box.
Revisiting A Highly Contrived Example
Let us use EOR to evaluate the hypothetical situation above, and see how it performs.
- Pebble: E - (A * R) = 10 - (1 * 1.64) = 8.36
- Boulder: E - (A * R) = 50 - (10 * 1.64) = 33.6
If we spend one Action to do Pebble, and spend the rest out of our day grinding AotB, then we will be eight Echoes and change richer than if we have simply ignored the opportunity. If we spend ten Actions to do Boulder, we will be more than thirty Echoes richer. By this metric, Boulder is around four times better. I don't know about you, but this aligns closer with my expectations.
A Real-World Example
NONE CAN ESCAPE THE OVERGOAT. Certainly not this post, which is now about Overgoats. Specifically, the Overgoat Opportunity Card. The options are actually fairly similar to the hypothetical above. We shall now calculate which of Overgoat-unlocked options is more profitable.
We start by defining the Opportunity, which is the Overgoat card. Next, we define the Choices. There are two Options on the card, but there are actually four Choices when one considers the possibility of using Second Chances or not. Following the example of the Wiki, I will evaluate a Second Chance as costing one Action to obtain it from wherever. For simplicity, I'll be using 50% and 75% as the success probabilities.
- Ask the Goat, No second Chance: 75% chance of 2.5 Echoes, 25% chance of 1 Echo. EOR = E - (A*R) = 2.125 - (1*1.64) = 0.485.
- Ask the Goat, Second Chance: 93.75% chance of 2.5 Echoes, 6.25% chance of 1 Echo. EOR = E - (A*R) = 2.406 - (2*1.64) = -.874
- Use the Goat, No Second Chance: 50% chance of 25 Echoes, 50% chance of 2.5 Echoes. EOR = E - (A*R) = 13.75 - (8*1.64) = 0.63
- Use the Goat, Second Chance: 75% chance of 25 Echoes, 25% chance of 2.5 Echoes. EOR = E- (A*R) = 19.375 - (9*1.64) = 4.615
I must say, these are not the results I was expecting. That means the science is working! I thought the numbers for using the Overgoat would be higher, but the Challenge seems to be well-tuned for its Action cost and Echo payout.
Note that technically, this is in accord with the results of the wiki, which say the EPA is similar for the two actions. It's just that the Boulder-ish option sustains that EPA over a larger number of Actions, giving a larger total payout.
Other Notes
I think that EOR is composable. By this, I mean that if we calculate (e.g.) the EOR of exchanging 15 CP of Connected: Hell for Brass, then we can plug that number straight in as an Echo value when calculating the EOR of something that gives CP Hell as a reward. I need to run through a scenario to verify, but I'm pretty sure it works out this way.
I want to eventually use this to calculate the value of Expeditions and Expedition Supplies, but it's late. That will wait for another day. In the meantime, I would appreciate any feedback, ideas, corrections, or disagreements anyone cares to make.
edited by PSGarak on 4/17/2017
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http://fallenlondon.com/Profile/PSGarak
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xKiv
Posts: 846
4/19/2017
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Kaigen wrote:
Am I calculating/understanding EOR correctly?
I think you got it mostly right.
One thing I would add is that 1 cp of SiC is actually worth a bit more, since you will often be able to use capering relicker (as a PoSI) for greater returns, when cashing in below SiC level 5. (at 14 cp - level 4 plus 4 points - IOW 1 cp below level 5 - that gives 0.74 EOR for 1 cp, and it even goes all the way up to 1.03 EOR/cp if you can cash in at exactly level 4. (But don't bother trying to align to that level, the extra actions are better spent on other things)).
Most connection-based conflict cards are poor for profit (siding with hell against church is one exception, assuming you don't mind the scandal), unless you want the connections, or the sideeffects.
As an example, applying the same to favours gives me the following interesting yields (at base 1.64 EPA) ...
Criminals: thieve's cache gives 12.4775 EOR/favor (but this is incorrect calculation, because it just assumes ~2.5 actions spent on getting the necessary dock favours ... so it's really closer to 3.42 EOR/favor for a 1:2.5 mix of criminals:docks; and it drops to only 2.6 when using only whispered hints grund at 150 hints/action)
... (alternative calculation: the other best cash-in for docks I have is vs. widow at 3.37, which means the criminal favour has about 12.4775-2.5*3.37=4.0525 EOR here)
Revolutionaries: flit cash-in is 3.88 EOR/f
Urchins: flit cash-in is 3.95 EOR/f (siding with hell against urchins is only 2.95 at 5 favours and 3.1 when done at 7 favours)
Tombs: 7.6 EOR/f via CoC gained in war of assassinss
Rubbery: 3.51 vs. revolutionaries (at 5 favours, but gives unaccounted-for scandal) or 3.25 vs. both constables and tombs (the last one also gives 10 carnival tickets, if you still have use for those)
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https://www.fallenlondon.storynexus.com/Profile/xKiv - a witchful, percussive, dangermous and shadowry scholar of coexplodence, hopsidirean, and walker of fallen kitties.
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Kaigen
Posts: 530
4/19/2017
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This also places the value of Connections that have a partially updated conflict card (Society, Widow, Constables) at about 0.05/cp.
I used it to investigate the EOR of accepting A Polite Invitation. Assuming base 1.64 EPA, Talk of the Town can be valued at 0.6448/cp. An efficient route through the party looks like...
Accept Invitation: 1.29
Arrive Late: 2.58
(If rare success, gossip about the Brass Ambassador =1.93)
Argue with the Contrarian: 2.58
Help the Tentacled Entrepreneur: 4.01 (Rubbery Favour plus 50 deep amber)
Evening Draws to a Close: 1.29
Taking your Leave: 1.5 (from 30 cp of Connected: Society, assuming TotT isn't high enough to cash in)
That comes out to an average of 2.21 echoes, giving an EOR of 0.57.
Interestingly, the calculated value of Tomb-Colonist Favours suggests that fueling the CoC grind is in fact the best use of said favours, though I still hesitate to make that the base rate grind, given that I seem to grind Collections faster than Favours overall. When one has twenty Collections waiting to be traded in, it's hard to argue that the best use of one's actions is grinding still more Collections.
edited by Kaigen on 4/19/2017
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Just a simple doctor with a chess habit. Publisher of The Flit Dispatch.
"One must remember that the impossible is, alas, always possible."
-Jacques Derrida
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